1. Membrane Trafficking: a) Membrane wave: In collaboration with Dr. Min Wu from National University of Singapore, we established a mechanochemical feedback model that accounts for the ultrafast rhythmic propagation (>1micron/sec) of the endocytic machine on plasma membrane in immune cells. Following our previous model, we found that immune cells exhibit stimulation-dependent traveling waves within the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and periphery membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that drive oscillations and render the cortex excitable. We show that this excitability manifests itself as waves of cortical proteins that are not limited by protein diffusions along membrane. Instead, the spatial gradient in the timing of the adjacent oscillations on the cortex gives the impression of spatial propagation. The resulting phase speed dictates the observed fast propagation speeds. We provide evidences that oscillatory membrane shape changes accompany such rhythms, excite further cortical activation, and potentiate propagation beyond the initial cortical activation site. Therefore, membrane shape change has underappreciated roles in setting high-speed signal transduction rhythms across the entire cortex. This paper is under review in Nature Communications. b) We constructed a mechanical model that describes the fate of post-fusion vesicle in exocytosis a key metabolic and signaling process for a cell. It involves vesicle fusion to the plasma membrane, followed by the opening of a fusion pore, and the subsequent release of the vesicular lumen content into the extracellular space. While most modeling efforts focus on the events leading to membrane fusion, how the vesicular membrane remodels after fusing to plasma membrane remains unclear. This latter event dictates the nature and the efficiency of exocytotic vesicular secretions, and is thus critical for exocytotic function. We provide a generic membrane mechanical model to systematically study the fate of post-fusion vesicles. We show that while membrane stiffness favors full-collapse vesicle fusion into the plasma membrane, the intravesicular pressure swells the vesicle and causes the fusion pore to shrink. Dimensions of the vesicle and its associated fusion pore further modulate this mechanical antagonism. We systematically define the mechanical conditions that account for the full spectrum of the observed vesicular secretion modes. Our model therefore can serve as a unified theoretical framework that sheds light on the elaborate control mechanism of exocytosis. Further, we established the collaboration with Dr. Roberto Weigert at NCI. With his experimental system of regulated exocytosis, we have been testing this model in particular the mechanistic role of the cage-like actomyosin structure in determining the fate of post-fusion vesicle. 2. Cell Division: a) SAC silencing in closed mitosis: We applied a similar SAC silencing mechanism as in open mitosis to closed mitosis, e.g. in budding yeast. We show that this spatial-temporal model can ensure the robustness of SAC silencing in closed mitosis. The poleward convection is unnecessary for the purpose of SAC silencing in closed mitosis, as conferred by the reduced dimensions of the mitotic apparatus and the closed confinement by nuclear envelope in closed mitosis. More importantly, the unique geometry of mitotic apparatus dictates that ploidy and sizes of nucleus and spindle pole body need to properly scale with each other in order for robust SAC silencing. This insight not only offers a unique and coherent explanation for diverse SAC silencing phenotypes observed in yeasts, but also suggests an evolutionary path that defines the karyotypes in present-day organisms and species. Further, we established the collaboration with Prof. Rong Li at Johns Hopkins U. With her experimental model system, the closed mitosis in budding yeast, we tested and further confirmed the key model predictions on the impact of chromosome number and the associated mitotic spindle geometry changes on the error rate of chromosome segregation. We are currently drafting our collaborative paper. b) ParA-mediated partition machinery: With Professor Jean-Yves Bouet from CRNS (France), we study how our proposed ParA-mediated partition mechanism that has been confirmed in vitro reconstitution study by the Kiyoshi lab plays out in vivo in E. Coli. In particular, we investigate the underlying mechanism of ParA oscillation between the separated nucleotides within a single cell. We show that this oscillation arises as a natural consequence that ParA-mediated partition machinery operates near a critical point that ensures the robustness of partition. Further, with Professor Anthony Vecchiarelli, we study how the same plasmid partition machinery drives a different motility of Carboxysomes in cyanobacteria, and how it contributes to carbon dioxide fixation. 3. Cell Motility: a) Fingering growth of focal adhesion: FA is heterogeneous within the same cell and across different cell types. Without a coherent model, this heterogeneity makes it difficult to analyze FA. We further extended our previous model on FA growth to explain the entire spectrum of FA growth pattern, in particular, FA could break into pieces during growth that eventually form finger-like parallel stripes. Our model establishes a unified theoretical framework that coherently accounts for FA growth under different conditions, and can serve as a guide for experiments. We are currently collaborating with Dr. Sergey Plotnikov to experimentally test the role of actin flux in shaping FA morphology. b) With Drs. Kandice Tanner (NCI) and Ajay Chitnis (NICHD), we interrogate the underlying control mechanism of collective cell migration in three-dimensional environment. We focus on the experimental model system of zebrafish, where the posterior Lateral Line primordium, a group of about a hundred cells, migrates under the skin, from near the ear to the tip of the tail, to pioneer formation of the zebrafish Lateral Line sensory system. This exercise is in the general regime of my cell migration project; its progress will both benefit from, and contribute to, our understanding of focal adhesion dynamics. This collaboration won the 2017 NIH DDIR Innovation award.